TUTORIAL – MODULE 3 SET THEORY
1). The combined membership of Accounts Society and Mathematical society is
100. Find the number of members in Mathematical society knowing that 60
members are the members of accounts society and 25 are the members of both
the institutions?
2). Out of 200 students in a management school 120 students read Indian
Economic Review and 100 read Harvard Business Review if the number of
students who read neither of the journals is 40 then find the number of students
who read both them?
3). In a class of 30 students, 14 has taken mathematics, 10 has taken
mathematics but not economics. Find the number of students who had taken
mathematics and economics also find the number of students who had taken
economics but not mathematics?
4). In an examination 100 students secured 80% and more marks in Economics
or Accounts. Out of these 70 obtained 80% and more marks in Economics and
20 in both Economics and Accounts. Then find how many of them have secured
80% and more marks in Accounts only?
5). 70 were polluted by Sulphur compounds, 60 were polluted by Lead and 80
were polluted by Fly Ash, 40 were polluted by Sulphur and Fly Ash, 30 were
polluted by Sulphur and Lead, 35 were polluted by Lead and Fly ash and 10
cities were polluted by all three compounds. Then find
(i) How many were polluted by one of three impurities?
(ii) How many cities are only polluted by Sulphur, Lead and Fly Ash?
(iii) How many of the cities are not polluted at all?
6). In a survey conducted in a town of 2000 population to see the readership of
newspaper, it has revealed that 1000 read Hindustan Times, 800 read Times of
India and 700 read Indian Express. If there was 400 who read both Hindustan
Times and Times of India, 300 who read both Times of India and Indian
Express, 500 read only Hindustan times and 100 read all the three papers. Then
find,
(i) How many read both Hindustan Times and Indian Express?
(ii) How of them read only one paper?
(iii) How many of them read none of the newspaper?
7). In a class of management course of 120 students appeared for their tri
semester examinations of Business Mathematics, Business Statistics and
Business Economics. After the results were declared it was found that 50 failed
in Business Mathematics, 48 failed in Business Statistics and 64 failed in
Business Economics. Moreover 18 failed in Business Mathematics alone, 12
failed Business Statistics alone and 10 in Business Statistics and Business
Economics then find
(i) How many failed in all the subjects?
(ii) How many passed in all the subjects?
(iii) How many passed in Business Economics alone?
8). The production manager of MIC House, M. Nuruddin has 95 workers in
Division-P, 80 workers in Division-Q and 120 workers in Division-R in his
firm. Three different types of products are produced in these three divisions and
workers in each division can easily perform the activities of that division.
However, out of these workers, 25 workers can perform the activities of P
and/or Q, 32 workers can perform the activities of Q and/or R, 39 workers can
perform the activities of P and/or R. There are only 12 workers who can
perform any activity of the three divisions. Due to change in the demand of the
product of three divisions, M. Nuruddin has to shift workers from one division
to another. In a 40-hour week, what would be the maximum labour hours in
each division that can be worked by this work force?